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Algebra II : Mathematical Relationships and Basic Graphs

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Example Questions

Example Question #2881 : Algebra Ii

What is the value of ?

Possible Answers:

Correct answer:

Explanation:

A factorial represents the product of all natural numbers less than a given number. Thus, 4! = 4*3*2*1 which gives us .

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Example Question #221 : Mathematical Relationships And Basic Graphs

Solve the Quadratic Equation.

4x^2 = 12x - 5

Possible Answers:

{5/2, 1/2}

2/5, 2

1, 1

3/4, 1/2

5/2, 2/5

Correct answer:

{5/2, 1/2}

Explanation:

First, move all terms to the left by subtracting the quantity on the right.

$4x^{2} = 12x - 5$

-(12x - 5) -(12x - 5) = 0

$= 4x^{2} - 12x + 5 = 0$

From here, factor the quadractic into two binomials and set each equal to zero.

= (2x - 5) (2x - 1)

2x - 5 = 0

+ 5 + 5

2x = 5

x = 5/2

2x - 1 = 0

+1 +1

2x = 1

x = 1/2

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Example Question #5 : Other Factorials

What is $\frac{10!}{7!}$ ?

Possible Answers:

720

810

4305

Correct answer:

720

Explanation:

Remember that factorial is defined as:

$n! = n \cdot (n-1)\cdot (n-2) \cdots \cdot (3)\cdot (2)\cdot (1)$

So using this definition, 10! = 10*9*8*7*6*5*4*3*2*1

And 7! = 7*6*5*4*3*2*1 .

So $\frac{10!}{7!} = \frac{10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}{7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1}$

The 7, 6, 5, 4, 3, 2, and 1 all cancel from both the numerator and denominator. So we're left with just 10*9*8 on top, which has a value of 720 .

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Example Question #2 : Other Factorials

How many -permutations (without repetition) are there when taking numbers from the set of numbers $\begin{Bmatrix} 16, 11, 9, 7, 14, 12, 18, 23, 1 \end{Bmatrix}$ ?

Possible Answers:

3024

729

504

Correct answer:

504

Explanation:

The elements of the set don't matter. Only the size of the set matters when determining permutations.

Our set contains 9 integers, so for the first number in our permutation, we have 9 choices.

After picking that number, because we're not allowed repetition, our second number is from 8 choices.

Our final number is from 7 choices.

Multiplying 9*8*7 gives us 504 .

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Example Question #77 : Factorials

What can n!(n+1) be expressed as?

Possible Answers:

n(n+1)

(n+1)!

n(n+1)!

n+1

Correct answer:

(n+1)!

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach . Since we are dealing with variables, let's analyze them. n+1 is definitely greater than in this situation because factorials are always positive numbers. If we took the difference between n+1 and we would get . This means after , the next biggest value is n+1 . Since we have and the next value multiplied is n+1 , we can conclude that (n+1)! will work since it incorporates values multiplied and also n+1 .

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Example Question #5 : Other Factorials

What is ?

Possible Answers:

Correct answer:

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $3\cdot 2\cdot 1$ .

Multiplying that out, we get .

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Example Question #3 : Other Factorials

What is ?

Possible Answers:

100

120

Correct answer:

120

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $5\cdot 4\cdot 3\cdot 2\cdot 1$ .

Multiplying that out, we get 120 .

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Example Question #4 : Other Factorials

What is $3! \cdot 4!$ ?

Possible Answers:

5040

144

256

Correct answer:

144

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $3\cdot 2\cdot 1$ . Multiplying that out, we get .

We also have . That is $4\cdot 3\cdot 2\cdot 1$ or .

Since we are multiplying the factorial, we multiply and to get 144 .

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Example Question #11 : Other Factorials

What is $\frac{6!}{4!}$ ?

Possible Answers:

$\frac{6}{5}$

Correct answer:

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ . We also have . That is $4\cdot 3\cdot 2\cdot1$ .

Since we are dividing the factorial, we can cancel out some terms.

Both the numerator and denominator have $4\cdot 3\cdot 2\cdot 1$ , and we can cancel those out. We are left with $6\cdot 5$ or 30.

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Example Question #223 : Mathematical Relationships And Basic Graphs

What is $\frac{7!}{30}$ ?

Possible Answers:

$\frac{1}{7}$

$\frac{1}{168}$

168

Correct answer:

168

Explanation:

A factorial means you are multiplying the number, with one less than previous number and you keep multiplying until you reach .

So, is $7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1$ . We are dividing by 30. With careful inspection, can be broken down to $6\cdot5$ .

If we cancel that out with the ones in the numerator, we have $7\cdot 4\cdot 3\cdot 2\cdot 1$ or 168 .

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Algebra II : Mathematical Relationships and Basic Graphs

Study concepts, example questions & explanations for Algebra II

All Algebra II Resources

Example Questions

Example Question #2881 : Algebra Ii

Example Question #221 : Mathematical Relationships And Basic Graphs

Example Question #5 : Other Factorials

Example Question #2 : Other Factorials

Example Question #77 : Factorials

Example Question #5 : Other Factorials

Example Question #3 : Other Factorials

Example Question #4 : Other Factorials

Example Question #11 : Other Factorials

Example Question #223 : Mathematical Relationships And Basic Graphs

All Algebra II Resources

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